We have investigated a generalized Villainrsquo;s model by varying the strength eegr; of the negative bond. We show that there exists a critical value eegr;c= (1)/(3) below which the twofold degeneracy disappears; the ground state becomes ferromagnetic. A detailed numerical study shows that, for a given eegr;eegr;c, the system exhibits in general, two distinct transitions: The low temperature one corresponds to Isinghyphen;type transition; the high temperature one corresponds to KT type. These two transitions seem to coincide in the Villainrsquo;s model (eegr;=1). Comparison with recent related models is presented.
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